The height of this cone is 3( 1 + [tex]\frac{l}{r}[/tex] ). Which have the same volume and surface area.
Given that
The value of the surface area (in square centimeters) of the cone is equal to the value of the volume (in cubic centimeters) of the cone.
The formula for the surface area S of a right cone is S=πr2+πrl, where r is the radius of the base and l is the slant height.
To find
The height of the cone.?
So, according to the question
We have,
The surface area of the cone = The volume of the cone.
We know that
The surface area of the cone,
S = πr²+πrl
And,
The volume of the cone,
V = [tex]\frac{1}{3} \pi r^2h[/tex]
So, from question
The surface area of the cone = The volume of the cone
S = V
Now, put the all values,
πr²+πrl = [tex]\frac{1}{3} \pi r^2h[/tex]
πr(r+ l) = [tex]\frac{1}{3} \pi r^2h[/tex]
(r+l) = [tex]\frac{1}{3}[/tex] × [tex]\frac{\pi r^2h}{\pi r}[/tex]
(r+l) = [tex]\frac{1}{3}[/tex] × rh
[tex]\frac{3(r+l)}{r}[/tex] = h
h = 3( [tex]\frac{r}{r} + \frac{l}{r}[/tex] )
h = 3( 1 + [tex]\frac{l}{r}[/tex] )
So the height of this cone is 3( 1 + [tex]\frac{l}{r}[/tex] ).
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7) In the given figure, PQR is an equilateral triangle with coordinates of Q and
R as (-2, 0) and (2, 0) respectively. Find the coordinates of the vertex P.
The coordinates of the vertex P is calculated as (0,2√3).
What is defined as the distance formula?The distances among two points as a characteristic of their coordinates are given by an algebraic expression (like coordinate system).
The Pythagorean theorem is used to derive distance formulae for points in rectangular coordinates in 2- and three-dimensional Euclidean space.Because it has a starting and ending point, a line segment can be graphed in both two-dimensional and three-dimensional coordinate planes.Because of the two-dimensional coordinate plane, the starting and stopping points can also be marked as two-dimensional coordinates (x₁, y₁) and (x₂, y₂), culminating in the distance formula as: d = √(x₂ - x₁)² + (y₂ - y₁)².Now, according to the given question;
The coordinates of the points Q and R is given as;
Q and R as (-2, 0) and (2, 0).
Now, as the all three points P,Q and R forms the equilateral triangle. Then, the distance of each side or the distance between two consecutive points are equal.
Calculate the distances between the points;
Distance between Q and R;QR = √(2 + 2)² + (0 - 0)²
QR = 4
Distance between Q and P;Let the coordinated of P be (x, y);
Then,
QP = √(x + 2)² + (y + 0)²
QP = QR = 4
4 = √(x + 2)² + (y)² ........(equation 1)
Distance between R and P;RP = √(x - 2)² + (y + 0)²
RP = QR = 4
4 = √(x - 2)² + (y)² ........(equation 2)
Equating equation 1 and 2.
√(x + 2)² + (y)² = √(x - 2)² + (y)²
Squaring both side;
(x + 2)² + (y)² = (x - 2)² + (y)²
x² + 4 - 4x + y² = x² + 4 - 4x + y²
Simplifying the equation;
x = 0.
Put the value of x in equation 1;
4 = √(x + 2)² + (y)²
y = 2√3.
Therefore, the coordinates of the point P are found to be (0, 2√3).
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25 points plus brainliest
Answer:
I believe it's B
4x - 5y = 16
Step-by-step explanation:
First you divide the whole term by -1 to get rid of negative in front of equation and then you add the c term (-16) to both sides to get the final answer.
I hope you get this right.
What is the next fraction in this sequence?Simplify your answer.
1/2, 4/7, 9/14, 5/7,....
Answer:
Step-by-step explanation:
[tex]\displaystyle\\\frac{1}{2},\ \ \frac{4}{7},\ \ \frac{9}{14},\ \ \frac{5}{7} ,\ \ ... \\\\\frac{1*7}{2*7} ,\ \ \frac{4*2}{7*2} ,\ \ \frac{9}{14}, \ \ \frac{5*2}{7*2} ,\ \ ...\\\\\frac{7}{14},\ \ \frac{8}{14} , \ \ \frac{9}{14},\ \ \frac{10}{14},\ \ \frac{11}{14},\ \ ...,\ \ \frac{6+n}{14} , \ \ n=1,\ 2,\ 3,\ ...[/tex]
Please help quickly!!!!
-3/5 - (-2/5) =
Write the answer as a fraction
Answer:
-1/5
Step-by-step explanation:
Minus a negative is plus.
-3/5 - (-2/5) =
= -3/5 + 2/5
= -1/5
On wednesday, a local hamburger shop sold a combined total of hamburgers and cheeseburgers. the number of cheeseburgers sold was three times the number of hamburgers sold. how many hamburgers were sold on wednesday?
The number of hamburgers sold on Wednesday is 141 and the number of cheeseburgers sold on Wednesday is 423
Although a part of your question is missing, you might be referring to this full question: On Wednesday, a local hamburger shop sold a combined total of 564 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Wednesday?
Total number of burgers sold on Wednesday = 564
Let the number of hamburgers sold on Wednesday be x
Let the number of cheeseburgers sold on Wednesday be y
Formulating the equation we get:
x + y = 564-----(1)
It is also given that, the number of cheeseburgers sold was three times the number of hamburgers. So,
y = 3x
Substituting y = 3x in equation (1) we get
x + 3x =564
4x = 564
x = 141
Putting x = 141 in equation (1) we get
y = 423
So, the number of hamburgers sold is 141 and the number of cheeseburgers sold is 423
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A sequence is ____ while a series is ______. A series is definite if_________, it is infinite if ________.
Answer: A sequence is a enumerated collection of objects in which repetitions are allowed/order matters while a series is a infinite series. A series is definite if its based on the concept of sequences.
A series could be finite or infinite because its mainly often represented in compact form which is also known as a sigma notation(∑)to indicate the summation involved. infinite series is the sum of an infinite sequence.
Step-by-step explanation:
How do I solve x for 2x+8=3x+10
To solve for x in: [tex]2x + 8 = 3x + 10[/tex]
Collect like terms
[tex]→8 - 10 = 3x - 2x \\ - 2 = x[/tex]
Therefore:
[tex]x = - 2[/tex]
The gardening store sells clay flower pots, which hold 8 litres of dirt, and ceramic flower pots, which hold 9 litres. Billy bought 8 flower pots, which will hold a total of 67 litres of dirt. How many of each type of flower pot did he buy?
According to the given statement;
Billy bought 8 flower pots, which will hold a total of 67 litres of dirt. The flower pot Billy bought his flower pot is x=5.
What is one variable equation?The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
For example, 2x+3=8 is a linear equation having a single variable in it.
What is a linear equation in math?A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction.According to given value ;
Let x = number of clay pots. Since Billy bought 8 pots in total , the number of ceramic pots Billy bought is 8-x
67 =(8 litre )*(x clay pots)+(9 litres)*(8-x);
By solving one variable equation;67=8x+72-9x
67=(-x)+72
-x =(-72+67)
( -x) = -5
x =5
Hence 8 litre of dirt clay pots is 5 then 9 litres of ceramic flower pot is is 3.
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the stock maeket fell 60 points over a period of four days. What was the average change in the stock market each day
Answer:
15 points
Step-by-step explanation:
It's 60 points over 4 days. We can divide 60 by 4, which is
15
Mr. Martin is giving a math test next period. The test, which is worth 100 points, has 29 problems. Each problem is worth either 5 points or 2 points. Write a system of equations that can be used to find how many problems of each point value are on the test.
Let x be the number of questions worth 5 points and let y be the number of questions worth 2 points.
Answer:
There are 14 problems worth 5 points and 15 problems worth 2 points.
Step-by-step explanation:
x - the number of 5 points worth problems
y - the number of 2 points worth problems
The test has 29 problems.
x+y=29x+y=29
The test is worth 100 points.
5x+2y=100
The system of equations:
x+y=29
5x+2y=100
The solution:
x+y=29 ∣×(−2)
5x+2y=100
Substract −2x−2y=−58 from 5x+2y=100
−2x−2y=−58
5x+2y=100
------------------
3x=42
3x/3 = 42/3
x=14
x+y=29
14+y=29
14+y-14 = 29 - 14
y=15
There are 14 problems worth 5 points and 15 problems worth 2 points.
PLEASE HELP BRANILY NEED THIS ASAP
Answer:
A. $7.46
Step-by-step explanation:
184.54 - 5.50 = 179.04
179.04 / 24 = 7.46
The answer WITHOUT SUBTRACTING THE DELIVERY FEE is: $7.69 (B).
If you're supposed to subtract the delivery fee, then the answer is $7.46 (A).
----------------------------------
Hope this helps!
Have a great day and God bless! :)
Question Progress
Homework Progress
24 / 63 Marks
a) Work out the value of (15)*× (√3)?
x
b) Work out the value of (19) × (√30) ?
x
1 14
豐
54%
Answer:
(a) 15
(b) 270
Step-by-step explanation:
Part (a)Given expression:
[tex]\left(\sqrt{5}\right)^2 \times \left(\sqrt{3}\right)^2[/tex]
[tex]\textsf{Apply the exponent rule}:\quad \left(\sqrt[n]{a}\right)^n=a,\quad \textsf{$n$ is odd or $a \geq 0$}[/tex]
[tex]\implies 5 \times 3[/tex]
Multiply the numbers:
[tex]\implies 15[/tex]
Part (b)Given expression:
[tex]\left(\sqrt[3]{9} \right)^3 \times \left(\sqrt{30}\right)^2[/tex]
[tex]\textsf{Apply the exponent rule}:\quad \left(\sqrt[n]{a}\right)^n=a,\quad \textsf{$n$ is odd or $a \geq 0$}[/tex]
[tex]\implies 9 \times 30[/tex]
Multiply the numbers:
[tex]\implies 270[/tex]
Now we have to,
→ work out the value for the following.
We know that,
→ square ( ²) and square root (√) gets cancelled each other.
→ cube ( ³) and cube root (³√) gets cancelled each other.
a) (√5)² × (√3)² = ?
→ (√5)² × (√3)²
→ 5 × 3 = 15
Thus, the answer is 15.
b) (³√9)³ × (√30)² = ?
→ (³√9)³ × (√30)²
→ 9 × 30 = 270
Thus, the answer is 270.
Write 7 times 100,000 + 6times 10,000+ 2times 1,000+ 5 times 100 + 8 times 1 in standered form
Draw a scaled copy of this polygon that has a perimeter of 30 units. what is the scale factor? explain how you know. help please
The scale factor is 3.
calculate scalar factor for given data?[tex]scale factor =\frac{scaled\ measure}{actual\ measure}[/tex]
∵ If sides of a polygon are changed by a scale factor 'a' then its perimeter is also changed by the same scale factor,
[tex]scale factor =\frac{scaled\ perimeter}{actual\ perimeter}[/tex]
The actual perimeter of the polygon = 10 unit,
Also, the scaled perimeter = 30 units
Hence,
[tex]scaled factor = \frac{30}{10} =3[/tex]
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ALMN is an isosceles triangle with LM = LN, LM LN, LM = 3x - 2, LN = 2x+1, and MN = 5x - 2. Find the length of MN.
Answer:
x = 3
Step-by-step explanation:
Marsha pays $30 each month for a car wash membership. Which of the following represents the total amount subtracted from her account after 8 months of having the membership?
|−30| − 8 = $22
−8|30| = −$240
8|−30| = $240
|−30| − |8| = $22
Marsha pay $30 each month for a car wash membership.
In one month Marsha pay $30
In eight month Marsha pay 8*$30 = $240
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Answer:
A. |-30| - 8 = $22
Step-by-step explanation:
You are told to subtract 30 and 8, and the 30 is represented as |-30| - 8 = $22
(if this is incorrect am sorry ;-;)
For the function h defined as h(x) = nx² + 28, n is a constant and h(3) = 1. What is the value of h(-6) ?
Answer:
Step-by-step explanation:
Step One
The first step is to find the value of n.
h(x) = n(x) + 28
h(3) = 1
That means that 1 is on the left and wherever there is an x on the right, it will have a value of 3
Step Two
Substitute values
1 = n(3) + 28
Step 3
Solve
1 = 3*n + 28 Subtract 28 from both sides
1 + - 28 = 3n Combine
-27 = 3n Divide both sides by 3
-27/3 = 3n/3
- 9 = n
Step 4
Let x = - 6 on the right side of the original equation.
h(-6) = 3*-6 + 28
h(-6) = -18 + 28
Answer
h(-6) = 10
Explain the properties used to solve inequalities and how they are different from properties of equality
The major difference between inequality and equality is that equality represents a particular value(s) while inequality represents a range of values that are in a specific direction.
What are the properties that are used to solve inequalities?This must be noted when solving questions on equality and inequality.
For example:
x = a means that the value of x is a. It represents a particular value which is a
x < a represents all the values that are less than a.
x ≤ a represents values from a and below.
x > a represents all the values that are greater than a
x ≥ a means that the values of x are greater than or equal to a.
From the examples given above, it is obvious that a change in the direction of the inequality sign changes the values of the data represented by the inequality.
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can u pls help me with my ixl :)
entering 60.00 into the price field entering 3.00 into the price of leather field entering 38.00 into the price of sneakers field
The required total of price area, leather field, and sneakers field is evaluated with the help of arithmetic operations as 102.
Given that,
Joining 60.00 into the price, area joining 3.00 into the price of the leather field entering 38.00 into the price of sneakers field,
The sum of the components is to be determined.
In mathematics, it deals with a number of procedures according to the statements. There are four primary arithmetic operators, addition, subtraction, multiplication, and division,
Here,
Joining 60.00 into the price area,
Joining 3.00 into the price of the leather field.
entering 38.00 into the price of sneakers field,
The sum = 60.00 + 3.00 + 38.00
The sum = 102
Thus, the required total of entries is evaluated with the help of arithmetic operations as 102.
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6 1/2 to quarts to cups
Answer:
26 cups
Step-by-step explanation:
1 quart = 4 cups
6 quarts x 4 cups = 24 cups
1/2 a quart = 2 cups
24+2= 26Answer:
12
Step-by-step explanation:
Order the square root of 70, negative 8.2 repeating, twenty five thirds, and negative eight and four sevenths from least to greatest.
negative eight and four sevenths, negative 8.2 repeating, square root of 70, twenty five thirds
negative eight and four sevenths, negative 8.2 repeating, twenty five thirds, square root of 70
negative 8.2 repeating, negative eight and four sevenths, twenty five thirds, square root of 70
negative 8.2 repeating, negative eight and four sevenths, square root of 70, twenty five thirds
The order from least to greatest is -8.222 <-7.43 < 8.333 < 8.366
The numbers given are:
The square root of 70 =√70 = 8.366
Negative 8.2 repeating = -8.222
Twenty five thirds = 25/3 = 8.333
Negative eight and Four sevenths = -8 and 4/7 = (-52)/7 = -7.43
So from least to greatest,
-8.222 <-7.43 < 8.333 < 8.366
That is, Negative 8.2 repeating < Negative eight and Four sevenths < Twenty five thirds < The square root of 70
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solve the equation for x if 2 to the power x = 8
Answer:
x=3Step-by-step explanation:
solve the equation for x if 2 to the power x = 8
2^x = 8
log(2x)=log(8)
x*log(2)=log(8)
x=((log(8))/((log(2))
x=3
----------------------------
check
2^3 = 8
2 * 2 * 2 = 8
8 = 8
the answer is good
la tarifa de un recorrido de taxi es de 7.25 de cargo fijo y de 7 por cada km recorrido determina la ecuación si p corresponde al valor del pago por x km recorridos
The equation that illustrates the amount to be paid for the number of kilometers will be 7.25 + 7x.
How to illustrate the information?Fixed rate for taxi = 7.25
Additional charges per kilometers = 7
Number of kilometers = x
Therefore, the equation that illustrates the amount to be paid for the number of kilometers will be:
= 7.25 + (7 × x)
= 7.25 + 7x
Therefore, the equation is 7.25 + 7x.
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If x = 45, y = 63, and the measure of AC = 4 units, what is the difference in length between segments AB and AD? Round your answer to the nearest hundredth. (1 point)
A
Hence , the difference in length between segments AB and AD is 1.17 units .
Trigonometric functions are referred to as Circular Functions will be merely outlined because the functions of associate angle of a triangle. It means the connection between the angles and sides of a triangle area unit given by these trig functions. the essential pure mathematics functions area unit circular function, cosine, tangent, cotangent, secant and trigonometric functionThe angles of circular function, cosine, and tangent area unit the first classification of functions of trig. and also the 3 functions that area unit cotan, secant and trigonometric function will be derived from the first functions. Basically, the opposite 3 functions area unit usually used as compared to the first pure mathematics functions.
The diagram of the given question is given below .
Applying sin rule in triangle ABC , we get
sin(x°) = AC/AB
sin(45°) = 4 / AB
1 /√2 = 4 / AB
AB = 4√2
AB ≈ 5.657
Similarly, apply sin rule in triangle ACD, we get
sin(y°) = AC /CD
sin(63°) = 4 / CD
AD = 4.489
Now distinction in lengths of AB and AD = 5.657 - 4.489
= 1.168
≈ 1.17
Therefore, distinction within the lengths of AB and AD are going to be 1.17 units.
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a whole number larger than 2 leaves a remainder of 2 when divided by each of the numbers 3, 4, 5 and 6.
A whole number larger than 2 leaves a remainder of 2 when divided by each of the numbers 3, 4, 5, and 6 is 62.
What are whole numbers?Whole numbers are numbers without fractions and consist of positive integers and zero. It is represented by the symbol "W," and the numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,...............Zero in its entirety represents nothing or a null value.To find the whole number:
LCM of 3, 4, 5, and 6 = 3 × 2 × 2 × 5 = 60Add the remainder 2 in 60: 60 + 2 = 62So, the whole number is 62.Therefore, a whole number larger than 2 leaves a remainder of 2 when divided by each of the numbers 3, 4, 5, and 6 is 62.
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a data set includes the following numbers: nineteen over 4, two and one fifth, 85%, and 3.24. part a: what is the order of the numbers from least to greatest?
The order of the numbers from least to greatest is:
85% < Two and one fifth < 3.24 < Nineteen over 4
The given data set of numbers are: nineteen over 4, two and one fifth, 85%, and 3.24
In order to compare these numbers, we will change all of them into float (decimal) format.
nineteen over 4 = 19/4 = 4.75
two and one fifth = 2 [tex]\frac{1}{5}[/tex] = 11/5 = 2.2
85% = 85/100 = 0.85
And 3.24 are the numbers set.
Now the order of numbers from least to greatest is clear.
Since 0.85 < 2.2 < 3.24 < 4.75, we can conclude
85% < 2 [tex]\frac{1}{5}[/tex] < 3.24 < 19/4
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a hot cup of tea is placed on a counter and left to cool. the temperature of the tea, in degrees fahrenheit (correct to the nearest degree), x minutes after the cup is placed on the counter is modeled by a continuous function t(x) for 0
Since T is continuous for [tex]0\leq x \le 10[/tex], [tex]\lim_{x \to 4} T(x)=T(4)[/tex] From the table:
[tex]\lim_{x \to 4} T(x)=172^{0}[/tex]
By continuous function, what do you mean?A continuous function in mathematics is one that causes the value of the function to continuously vary as the input changes over time. This indicates that there aren't any discontinuities or sudden changes in value. In other words, a function is continuous if and only if its graph is devoid of any gaps or breaks. It is simple to predict where it won't be continuous for many functions. Where we have operations like division by zero or logarithms of zero, functions won't be continuous. Examples of continuous functions over the set of all real numbers are polynomial functions, exponential functions, and the sin and cosine graphs.
For the final answer the table is to be checked and all the values are written.
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(-4,5) is translated by the vector (-1/10). What coordinate would it be at?
The coordinates of the image of the point (- 4, 5) is (- 5, 15).
What is the image of a coordinate by using a translation?
In this question we find the coordinates of the original point and the translation vector. Please notice that translations are examples of rigid transformations, meaning that Euclidean distance is conserved in the resulting image. A translation can be done by the following formula:
P'(x, y) = P(x, y) + T(x, y)
Where:
P(x, y) - Original pointT(x, y) - Translation vectorP'(x, y) - Resulting pointIf we know that P(x, y) = (- 4, 5) and T(x, y) = (- 1, 10), then the resulting point is:
P'(x, y) = (- 4, 5) + (- 1, 10)
P'(x, y) = (- 5, 15)
RemarkThere is a typing mistake in the statement. Correct form is shown below:
(- 4, 5) is translated by the vector (- 1, 10). What coordinate would it be at?
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4. Juan has 28 paperback books that measure
re 1 1/4 inches each, how many books will fit on one
shelf if each shelf measures 30 inches?
Answer:
24 books can fit on 1 shelf.
Step-by-step explanation:
Question: Juan has 28 paperback books that measure 1 and 1/4 inches each. How many books will fit on one shelf if each shelf measures 30 inches?
Step-by-step:
We know that each book is 1 and 1/4 inches each. It might be easier to convert the fraction into a decimal.
1/4 inches is 1 divided by 4 which equals to 0.25 inches
1 inch + 0.25 inches = 1.25 inches
so, 1 and 1/4 inches = 1.25 inches
To find out how many books fit on a shelf, we need to find: length of 1 bookshelf divided by length of 1 book
We know that one bookshelf is 30 inches and 1 book is 1.25 inches
so, 30/1.25 or 30 divided by 1.25 = 24
Therefore, 24 books can fit on 1 shelf.